Mars Crater Study-1
This article was written as a practice exercise with reference to the information provided in the COURSERA course, specifically the Mars Crater Study.
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My program,
import pandas as pd
import statsmodels.formula.api as smf
# Set display format
pd.set_option('display.float_format', lambda x: '%.2f' % x)
# Read dataset
data = pd.read_csv('marscrater_pds.csv')
# Convert necessary variables to numeric format
data['DIAM_CIRCLE_IMAGE'] = pd.to_numeric(data['DIAM_CIRCLE_IMAGE'], errors='coerce')
data['DEPTH_RIMFLOOR_TOPOG'] = pd.to_numeric(data['DEPTH_RIMFLOOR_TOPOG'], errors='coerce')
# Perform basic linear regression analysis
print("OLS regression model for the association between crater diameter and depth")
reg1 = smf.ols('DEPTH_RIMFLOOR_TOPOG ~ DIAM_CIRCLE_IMAGE', data=data).fit()
print(reg1.summary())
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Output results,
Dep. Variable: DEPTH_RIMFLOOR_TOPOG
R-squared:0.344
Model: OLS
Adj. R-squared:0.344
Method:Least Squares
F-statistic:2.018e+05
Date:Thu, 27 Mar 2025
Prob (F-statistic):0.00
Time:14:58:20
Log-Likelihood:1.1503e+05
No. Observations:384343
AIC:-2.301e+05
Df Residuals:384341
BIC:-2.300e+05
Df Model: 1
Covariance Type:nonrobust
coef std err t P>|t| [0.025 0.975]
Intercept 0.0220 0.000 70.370 0.000 0.021 0.023
DIAM_CIRCLE_IMAGE
0.0151 3.37e-05 449.169 0.000 0.015 0.015
Omnibus:390327.615
Durbin-Watson:1.276
Prob(Omnibus):0.000
Jarque-Bera (JB):4086668077.223
Skew: -3.506
Prob(JB):0.00
Kurtosis:508.113
Cond. No.10.1
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Results Summary:
Regression Model Results:
R-squared: 0.344, indicating that the model explains approximately 34.4% of the variability in crater depth.
Regression Coefficient (DIAMCIRCLEIMAGE): 0.0151, meaning that for each unit increase in crater diameter, the depth increases by an average of 0.0151 units.
p-value: 0.000, indicating that the effect of diameter on depth is statistically significant.
Intercept: 0.0220, which is the predicted crater depth when the diameter is zero.
Conclusion:
The analysis shows a significant positive association between crater diameter and depth. While the model provides some explanatory power, other factors likely influence crater depth, and further exploration is recommended.